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Simplifying -5a2 + -4a + 21 = 0 Reorder the terms: 21 + -4a + -5a2 = 0 Solving 21 + -4a + -5a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -4.2 + 0.8a + a2 = 0 Move the constant term to the right: Add '4.2' to each side of the equation. -4.2 + 0.8a + 4.2 + a2 = 0 + 4.2 Reorder the terms: -4.2 + 4.2 + 0.8a + a2 = 0 + 4.2 Combine like terms: -4.2 + 4.2 = 0.0 0.0 + 0.8a + a2 = 0 + 4.2 0.8a + a2 = 0 + 4.2 Combine like terms: 0 + 4.2 = 4.2 0.8a + a2 = 4.2 The a term is 0.8a. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8a + 0.16 + a2 = 4.2 + 0.16 Reorder the terms: 0.16 + 0.8a + a2 = 4.2 + 0.16 Combine like terms: 4.2 + 0.16 = 4.36 0.16 + 0.8a + a2 = 4.36 Factor a perfect square on the left side: (a + 0.4)(a + 0.4) = 4.36 Calculate the square root of the right side: 2.088061302 Break this problem into two subproblems by setting (a + 0.4) equal to 2.088061302 and -2.088061302.Subproblem 1
a + 0.4 = 2.088061302 Simplifying a + 0.4 = 2.088061302 Reorder the terms: 0.4 + a = 2.088061302 Solving 0.4 + a = 2.088061302 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + a = 2.088061302 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + a = 2.088061302 + -0.4 a = 2.088061302 + -0.4 Combine like terms: 2.088061302 + -0.4 = 1.688061302 a = 1.688061302 Simplifying a = 1.688061302Subproblem 2
a + 0.4 = -2.088061302 Simplifying a + 0.4 = -2.088061302 Reorder the terms: 0.4 + a = -2.088061302 Solving 0.4 + a = -2.088061302 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + a = -2.088061302 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + a = -2.088061302 + -0.4 a = -2.088061302 + -0.4 Combine like terms: -2.088061302 + -0.4 = -2.488061302 a = -2.488061302 Simplifying a = -2.488061302Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.688061302, -2.488061302}
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